4 ideas
| 18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
| Full Idea: On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result. | |
| From: Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3 | |
| A reaction: This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent. |
| 21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
| Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people." | |
| From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork. |
| 16473 | Modal Rationalism: conceivability gives a priori access to modal truths [Chalmers, by Stalnaker] |
| Full Idea: Chalmers' 'modal rationalist' is one who identifies what is possible with what is conceivable; the central claim of the doctrine is that we have a priori access to modal truth. | |
| From: report of David J.Chalmers (Does Conceivability Entail Possibility? [2002]) by Robert C. Stalnaker - Mere Possibilities 5 | |
| A reaction: A helpful clarification, as I can now see how hopelessly and utterly wrong Chalmers is (about almost everything), and I find my confidence in any sort of genuine a priori knowledge (except of conceptual relations) dwindling by the minute. |
| 19258 | Evaluate primary possibility from some world, and secondary possibility from this world [Chalmers, by Vaidya] |
| Full Idea: For Chalmers, that water is XYZ is 'primary possible' (a priori, or conceptually), because it is true in some world considered as actual. It is 'secondary impossible', when it is evaluated from the Earth as actual. | |
| From: report of David J.Chalmers (Does Conceivability Entail Possibility? [2002]) by Anand Vaidya - Understanding and Essence Intro | |
| A reaction: [compressed] This is Chalmers' account of how we can know possibility from conceivability, via his two-dimensional semantics (see alphabetical themes). |